This chapter will discuss settings in which the dependent variable we seek to
model takes on a range of values that are restricted, broadly defined as
limited dependent variable models. Within the class of limited
dependent variables, a special case arises when the outcome is no longer a
continuous measure but a discrete variable. Such data often arise as
individuals making a choice from a set of potential discrete outcomes, thus
earning the name discrete choice models. The most common case of
such models occurs when \(y\)  is a binary response and takes on the values zero
and one, indicating whether or not the event has occurred, giving rise to
binary modelsBinary models are special cases of both
ordinal and multinomial models with more than two categories.. Consider for
example, participation in the labour force, whether or not an individual will
buy a vehicle, whether or not a country is part of free trade agreement. In
other cases, \(y\)  may take on multiple (more than two) discrete values, with
no natural ordering. Consider for example, choice of brand of toothpaste or
mode of transportation. These are referred to as multinomial models.
We refer the readers to [1]} for a detailed discussion on
multinomial models, their estimation and inference. Further, there could be
situations where \(y\)  takes on multiple (more than two) discrete values that
are inherently ordered or ranked. For example, scores attached to opinion on
surveys (oppose, neutral, support), classification of educational attainment,
or ratings on bonds. These give rise to ordinal models or
ordered choice models. Here, we discuss four discrete choice models
– ordinal probit, ordinal logit, binary probit and binary logit models.
